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Studia Logica

, Volume 53, Issue 1, pp 21–28 | Cite as

P1 algebras

  • Renato A. Lewin
  • Irene F. Mikenberg
  • Maria G. Schwarze
Article

Abstract

In [3] the authors proved that the deductive systemP1 introduced by Sette in [6] is algebraizable. In this paper we study the main features of the class of algebras thus obtained. The main results are a complete description of the free algebras inn generators and that this is not a congruence modular quasi-variety.

Keywords

Mathematical Logic Computational Linguistic 
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References

  1. [1]
    W. J. Blok andD. Pigozzi,Algebraizable logics Memoirs AMS. 77 396 (1989).Google Scholar
  2. [2]
    N. C. A. da Costa,On the theory of inconsistent formal systems Notre Dame Journal of Formal Logic 15 4 (1974), pp. 497–510.Google Scholar
  3. [3]
    R. A. Lewin, I. F. Mikenberg andM. G. Schwarze,Algebraization of paraconsistent logic P 1 The Journal of Non-Classical Logic 7 1/2 (1990).Google Scholar
  4. [4]
    R. A. Lewin, I. F. Mikenberg andM. G. Schwarze,C 1 is not algebraizable Notre Dame Journal of Formal Logic 32 4 (1991), pp. 609–611.Google Scholar
  5. [5]
    C. Mortensen,Every quotient algebra for C 1 is trivial Notre Dame Journal of Formal Logic 21 4 (1980), pp. 694–700.Google Scholar
  6. [6]
    M. A. Sette,On the propositional calculus P 1 Mathematica Japonicae 16 (1973), pp. 173–180.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Renato A. Lewin
    • 1
  • Irene F. Mikenberg
    • 1
  • Maria G. Schwarze
    • 1
  1. 1.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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